Statement-1: Let A and B be two sets having m and n elements respectively such that `m lt n`. Then, Number of surjections from A to B `=sum_(r=1)^(n) ""^(n)C_(r) (-1)^(n-r) r^(m)` Statement-2: If `f:A to B` is a surjection, then every element in B has a pre-image in A.A. 1B. 2C. 3D. 4

Statement-1: Let A and B be two sets having m and n elements respectiv

1.	Statement-1: Let A and B be two sets having m and n elements respectively such that `m lt n`. Then, Number of surjections from A to B `=sum_(r=1)^(n) ""^(n)C_(r) (-1)^(n-r) r^(m)` Statement-2: If `f:A to B` is a surjection, then every element in B has a pre-image in A.A. 1B. 2C. 3D. 4
Answer» Correct Answer - D Since B has more element than A. So, m elements in set A can be related to at most m elements in B. Consequently, remaining (n-m) elements in B will not have their pre-images in A. So, it is not possible to define an onto function from A to B. Hence, statement-1 is a false. However, statement-2 is true.